## Arts & Sciences Electronic Theses and Dissertations

Spring 5-15-2019

#### Author's School

Graduate School of Arts and Sciences

Economics

#### Degree Name

Doctor of Philosophy (PhD)

Dissertation

#### Abstract

In my dissertation, I focus on theoretical affine term structure models and the development of Bayesian econometric methods to estimate them.

In the first Chapter, we address the question of which unspanned macroeconomic factors are the best in the class of macro-finance Gaussian affine term structure models. To answer this question, we extend Joslin, Priebsch, and Singleton (2014) in two dimensions. First, following Ang and Piazzesi (2003) and Chib and Ergashev (2009), three latent factors, instead of the first three principal components of the yield curve, are used to represent the level, slope and curvature of the yield curve. Second we postulate a grand affine model that includes all the macro-variables in contention. Specific models are then derived from this grand model by letting each of the macro-variables play the role of a relevant macro factor (i.e. by affecting the time-varying market price of factor risks), or the role of an irrelevant macro factor (having no effect on the market price of factor risks). The Bayesian marginal likelihoods of the resulting models are computed by an efficient Markov chain Monte Carlo algorithm and the method of Chib (1995) and Chib and Jeliazkov (2001). Given eight common macro factors, our comparison of 28=256 affine models shows that the most relevant macro factors for the U.S. yield curve are the federal funds rate, industrial production, total capacity utilization, and housing sales. We also show that the best supported model substantially improves out-of-sample yield curve forecasting and the understanding of term-premium.

The second Chapter considers the question of which unspanned macro factors can improve prediction in arbitrage-free affine term structure models and convert return forecasts into economic gains. To achieve this, we develop a Bayesian framework for incorporating different combinations of macro variables within an affine term structure framework. Then each specific model within the framework is evaluated statistically and economically. For the statistical evaluation, we examine its out-of-sample yield density forecasting. The economic value of each model is compared in terms of the bond portfolio choice of a Bayesian risk- averse investor. We consider two main kinds of macro factors: representative macro factors in Chib et al. (2019) and principal component macro factors in Ludvigson and Ng (2009b). Our empirical results show that regardless of macro dataset we use(either Chib et al. (2019) or Ludvigson and Ng (2009b)), macro factor in real economic activity, financial sector and price index will help generate notable gains in out-of-sample forecast. Such gains in predictive accuracy translate into higher portfolio returns after accounting for estimation error and model uncertainty. In contrast, incorporating redundant macro variables into the affine term structure models can even decrease utility and prediction accuracy for investors. In addition, given the data sample we consider in the Chapter, we also find that principle component factors can perform relatively better than representative macro factors in terms of certainty equivalence return (CER).

The third Chapter compares the posterior sampling performance of No-U-Turn sam- pler(NUTS) algorithm and tailored randomized-blocking Metropolis-Hastings (TaRB-MH) for macro-finance affine Term structure models. We conduct empirical experiments on 3 affine term structure models with the U.S. yield curve data. For each experiment, we examine the sampling efficiency of model parameters, factors, term premium, predictive yields,etc. Our emprical results indicate that the TaRB-MH substantially outperforms the NUTS method

in terms of the convergence and efficiency in posterior sampling. Furthermore, we show that NUTS’ inefficiency in simulating the affine term structure models will be robust given different initial values for the algorithm.

English (en)

Siddhartha Chib

#### Committee Members

Siddhartha Chib, Werner Ploberger, Guofu Zhou, Yongseok Shin,